Two-dimensional electron gas of the ${\mathrm{In}}_2{\mathrm{O}}_3$ surface: Enhanced thermopower, electrical transport properties, and reduction by adsorbates or compensating acceptor doping

${\mathrm{In}}_2{\mathrm{O}}_3$ is an $n$-type transparent semiconducting oxide possessing a surface electron accumulation layer (SEAL) like several other relevant semiconductors, such as InAs, InN, ${\mathrm{SnO}}_2$, and ZnO. Even though the SEAL is within the core of the application of ${\mathrm{In}}_2{\mathrm{O}}_3$ in conductometric gas sensors, a consistent set of transport properties of this two-dimensional electron gas (2DEG) is missing in the present literature. To this end, we investigate high-quality single-crystalline as well as textured doped and undoped ${\mathrm{In}}_2{\mathrm{O}}_3$(111) films grown by plasma-assisted molecular beam epitaxy to extract transport properties of the SEAL by means of Hall effect measurements at room temperature while controlling the oxygen adsorbate coverage via illumination. The resulting sheet electron concentration and mobility of the SEAL are $\approx 1.5\times {10}^{13}{\mathrm{cm}}^{-2}$ and $\approx 150{\mathrm{cm}}^2/\mathrm{Vs}$, respectively, both of which are strongly reduced by oxygen-related surface adsorbates from the ambient air. Our transport measurements further demonstrate a systematic reduction of the SEAL by doping ${\mathrm{In}}_2{\mathrm{O}}_3$ with the deep compensating bulk acceptors Ni or Mg. This finding is supported by x-ray photoelectron spectroscopy (XPS) measurements of the surface band bending and SEAL electron emission. Quantitative analyses of these XPS results using self-consistent, coupled Schrödinger-Poisson calculations indicate the simultaneous formation of compensating bulk donor defects (likely oxygen vacancies), which almost completely compensate the bulk acceptors. Finally, an enhancement of the thermopower by reduced dimensionality is demonstrated in ${\mathrm{In}}_2{\mathrm{O}}_3$: Seebeck coefficient measurements of the surface 2DEG with partially reduced sheet electron concentrations between $3\times {10}^{12}$ and $7\times {10}^{12}{\mathrm{cm}}^{-2}$ (corresponding average volume electron concentration between $1\times {10}^{19}$ and $2.3\times {10}^{19}{\mathrm{cm}}^{-3}$) indicate a value enhanced by $\approx 80\%$ compared to that of bulk Sn-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ with comparable volume electron concentration.

Figure 1

Schematic representation of the band alignment for (a) intentional doping with deep bulk acceptors and the corresponding compensation of the bulk donors and the SEAL, (b) unintentionally doped ${\mathrm{In}}_2{\mathrm{O}}_3$, and (c) unintentional compensation of the SEAL due to adsorption of acceptorlike oxidizing species. The dots indicate that the donor and acceptor levels continue towards the surface of the film while maintaining a constant distance to the band edges. The difference $(N_{\mathrm{D},\mathrm{S}}^{+}-N_{\mathrm{A},\mathrm{S}}^{-})$ of the 2D concentration of charged surface donors and acceptors provides a net surface charge $N_{\mathrm{SS}}$.

Figure 2

Schematic representation of the carrier systems in the films under study. The substrate is insulating, while it has been shown that the samples under study possess a strong interface carrier system along with the bulk of the film and the SEAL [24]. (a) All carrier systems included in the as-grown film, (b) depleted SEAL in the plasma-oxidized film, (c) extracted SEAL by the multilayer method of Refs. [46] and [47].

Figure 3

Transport properties of the SEAL as a function of compensating acceptor concentration $N_{\text{Ni/Mg}}$: sheet conductance $G_{\mathrm{S}}$, sheet electron concentration $n_{\text{S}}$, and Hall electron mobility ${\mu }_{\mathrm{S}}$. The open symbols represent the extracted data without the effect of air adsorbates [as in Eq. (3)], whereas the closed symbols correspond to the extracted SEAL transport properties with air adsorbates [Eq. (2)].

Figure 4

X-ray photoelectron spectra of the valence band and occupied conduction-band states of the single-crystalline unintentionally doped (UID) and Ni-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ films (Ni concentration as indicated). For the Ni-doped films, only the VB edge is shown for clarity and to depict the occurring energy shift and additional intragap states, as the shape of the complete VB spectra at higher binding energies is similar to that of the UID sample. The magnified region on the right has been smoothed (nine-point locally weighted smoothing).

Figure 5

Change of valence-band maximum $\mathrm{\Delta }\mathrm{VBM}$ (blue, closed points) and relative SEAL induced electron emission (red, open points) as a function of acceptor concentration $N_{\mathrm{Ni}/\mathrm{Mg}}$ extracted from the XPS spectra. The relative electron emission values from the SEAL have been normalized with respect to the unintentionally doped reference sample. The inset shows the relative SEAL intensity (red axis) vs $\mathrm{\Delta }\mathrm{VBM}$ (blue axis), including data from both ${\mathrm{In}}_2{\mathrm{O}}_3$:Ni and ${\mathrm{In}}_2{\mathrm{O}}_3$:Mg.

Figure 6

Conduction band edge distributions (a) and electron concentration profiles (b) of UID (i) and acceptor-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ (vii, ix) calculated by Schrödinger-Poisson calculations considering a deep acceptor level and constraints as shown in Table 1. Inset (b.1) depicts the electron concentration for two different $n_{\mathrm{S}}$ cases in linear scale based on the experimental results from the XPS analysis of the Ni-doped films, whereas inset (b.2) shows the wave functions of the bound states ${\psi }_{1,2,3}$ of UID ${\mathrm{In}}_2{\mathrm{O}}_3$ (case i) due to the potential induced by surface band bending. The energies corresponding to these states are $E_1=-137.24\mathrm{meV}, E_2=-0.22\mathrm{meV}$, and $E_3=36.33\mathrm{meV}$. The percentages specified in the figure represent the relative contributions of each wave function to the 2DEG.

Figure 7

Top: Seebeck coefficient as a function of the surface sheet electron concentration measured by Hall effect experiments in the vdP arrangement. Bottom: comparison of the volume electron concentration of the SEAL with that of bulk ITO films and solution of the Boltzmann transport equation for $m^{*}=0.3m_{\mathrm{e}}$ from the work of Preissler et al. [45] (Fig. 9 therein).